Gargle with warm salt water. Very easy to make and does work. It'll ease the cough as well as kill some of the germs in there.
Also, be sure you're drinking a lot of water. Keeping yourself hydrated will prevent the scratchiness in there that's causing the cough.
And, watch it. If it goes on too long, you might want to see a doctor to get something prescribed.
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Cats know what we feel. They don't care, but they know.